To prove something, you must provide evidence of its existence. The burden of proof lies upon the assertion of existence. To prove I have a dog, for example, is a simple matter - I would simply show you the dog. Reasonable enough an induction, to see a dog that I show you, and conclude I have a dog. To prove the existence of an object, you must simply display phenomena which can be best described by the existence of said object. To prove the sun exists, I can point to the burning ball in the sky, and note how it warms my skin. However, how would I go about proving I do not have a dog? Think on your own for a moment here. IMHO, short of possessing complete omniscience, I cannot prove such a thing. You might say, on a similar tangent, that you believe in God because you have never seen otherwise. Well, have you ever seen anything contradicting me owning a dog? Anything contradicting a pack of invisible transient rabid interplanar Teletubbies that follow you wherever you go? I certainly hope you do not assume every man you meet is Elvis, until you have reason to believe otherwise. You would be going about things backwards, my friend.

No, I cannot prove to you the nonexistence of God. But I am equally helpless to disprove the existence of those pesky interplanar Teletubbies... absurd as it is. And this is why skepticism assumed the following rule:

Atheism, as it exists today, is not a belief system.
...
Until you have reason to believe any given thing exists,
you must assume its nonexistence.

The very nature of assumption is a belief system. There is no proof for the thing assumed, there is nothing in the scientific method that states that that if there is no proof for A, then not A must be assumed. Assumption is belief. Webster1913 even does a good job describing belief:

To disprove the existence of God, there must be similar evidence of non-existence. Proving the existence of anything gets into very tricky (and either very interesting or non-interesting depending on your philosophical bend) metaphysics. There is an entire branch of philosophy that believes that I am the only mind in existence - its called solipsism. Arguing with such individuals is a complete waste of time - they believe (many claim to have proof) you to be a figment of their imagination - as is everything else.

To make any statement, the burden of proof is upon the individual making the statement to prove that it is such. With any skeptic worth his or her weight in ideas, assumptions are forbidden. The quest for knowledge is not over when it has been shown that 'A cannot be proved', and certainly it does not follow that 'not A must be true'. This is the credo of skeptic - academic skepticism and Pyrrhonism both agree upon this point: The skeptikoi continues to search.

Given the evidence at hand, the belief in a God or gods is just as reasonable as the belief in the non-existence of these entities.

The pursuit of truth does not and cannot end with 'it is impossible to know'.

The essence of If you cannot prove A then you must assume not A is true has a great deal of problems.

The first of these problems is when not A cannot be proven either. If there is no proof for not A, must we also assume that A is true? Both of the statements cannot be true at the same time. I have no reason to believe of the existence of a mind of a noder who simply copies and pastes the works of others, must I assume that it does not exist?

This approach leads to absurdity with numerous other classical problems in philosophy. Of these, my favorite is the 'red green inversion'.

Can it be determined if what I perceive as 'red' another individual will perceive as 'green', and what he perceives as 'red', I perceive as 'green'. Now, we both call the colors the same, its just that the mind-state that is caused from the perception is reversed.

Many philosophers puzzle at this for awhile, some call it a silly problem because you can't ever figure out if that is the case or not (some jokingly argue that this is the reason for bad fashion sense). Now, applying the rule above, if we cannot determine if if we perceive colors the same, we must assume that we perceive them differently - without any evidence backing it.

When there is no proof for something, the correct response is not to assume that something is not the case, but rather suspend judgment and continue to seek. If there is no proof for or against it, then feel free to believe whatever you wish.

One of the interesting parts of philosophy (again, depending on your bend) is the argument that there is no interesting philosophical conclusion that can be proven beyond the possibility of doubt. That there has been no argument for the existence (or non-existence) of God does not weaken (or strengthen) the case for God's existence. Simply, this places the question of God's existence in the same set of questions as the nature of an external, mind-independent world or the question of how we know other individuals have minds at all.

Many philosophers have taken up the challenge of a proof of God's existence or non-existence. Some have even tried to prove the impossibility of the proof for or against the existence of God (see Critique of Pure Reason). However, there are reasonable proofs on both sides of the argument. The question is not one of "overwhelming proof" but rather "consistent with the evidence and of explanatory value".

Throughout the history of science, observations where made about cosmology going from a flat earth through a geocentric universe to Kepler and elliptical orbits about the sun. None of these beliefs were unreasonable at the time of their conception and provided explanatory value for the state of the world. Ptolemy's system worked for centuries and provided a great deal of explanatory value.

Today, we have quantum theory and super strings that we have no proof of. The stuff of quarks has only been theorized - there is nothing to say that that is the actual way it works. And yet, we believe in them because they are consistent with the evidence and provide explanatory value for us.

If it is reasonable for us to believe in scientific theories that have no proof but rather observations consistent with the theory, it is just as reasonable for people to believe or disbelieve in the existence of God or gods.

One of the problems that people appear to be having here, is the
question of belief. Belief is one of the requisites for
knowledge, along with truth and justification. However, lacking
proof of the truth we are left with the issue of 'reasonable belief'.

What does it take to have a 'reasonable' belief. Here, the
requirements are even less strenuous than the justification for knowledge.

If you have an argument that convinces you, or as I've said above
an explanation that addresses the evidence, then this is a reasonable
belief. To a child, who is told by an authority that Santa Claus
exists, the belief in Santa is a reasonable one.

Santa is written on the from on presents.

Santa gets mail sent to him (it doesn't come back)

Santa listens to your wishes when sitting on your lap, and you
get those presents

Santa is part of the weather report on Christmas Eve

etc...

Does not the belief in existence of Santa Claus fit the requirements for
'consistent with the evidence and of explanatory value'?

Similarly, the belief in God is reasonable. There are a vast many people
who hold that His existence is consistent with that of the evidence
of the way the world works and provides explanation as to the way the
world will continue to work.

In both of these cases, the issue of 'truth' does not come into play.
Most of us would actually be worried about a young child skeptical to
the point of not believing in Santa when given such a preponderance of
evidence (especially if they haven't been told that he doesn't exist).
Likewise, religious authorities are often concerned with people who
do not believe in God in what they consider a similar set of evidence.

We are not dealing with a criminal court here. The criteria for
reasonable belief is not that of "beyond all reasonable doubt" - that
is knowledge. Only a very few deluded individuals will make claims to
having knowledge of the existence or non-existence of God.
Even in a jury, jurors often have the responsibility of saying
"Although I believe that A, it has not been proven so I must say
not A".

"Some methodological atheists formulate the principle by saying that the burden of proof is always on any person making an existence claim, since, from a logical point of view, existence claims are only capable of proof, not disproof. No one has ever proven the nonexistence of Santa Claus, or elves, or unicorns, or anything else, simply because the very logic of an unrestricted existential proposition prohibits its disproof. It is impossible to go all over the universe and show that, for example, there are no elves anywhere. For this reason, rational methodology calls for us to deny the existence of all those things which have never been shown to exist. That is why we all regard it rational to deny the existence of Santa Claus, elves, unicorns, etc. And since God is in that same category, having never been shown to exist, it follows that rational methodology calls for us to deny the existence of God."

"Given the evidence at hand, the belief in a God or gods is just as reasonable as the belief in the non-existence of these entities."

Statements like the above are hypocricy, as a simple observation of the person stating them will show. No one grants equal plausibility to existence and nonexistence of Romulans, Ur-Quan, Satan, tooth fairies, vampires, etc. If one were to do that, one would be incapable of acting in this world. In order to act, one must form an assumption: either act as if this entity exists, or as if it doesn't. Militant agnostics and sceptics refute their own words by their actions--every time they act as if Zeus doesn't exist.

Take for example, an apple that is an orange. This sounds crazy, and intuitively, we know this object doesn't exist. Why, you might ask? Because its existence contradicts itself. If it is an apple, it is not an orange, and vice versa; we have an internal inconsistency that is immediately apparent. To say it explicitly: one of the properties of being an orange could be called not-appleness, and one of the properties of being an apple could be called appleness. Appleness and not-appleness being properties of the same object is a contradiction, therefore the existence of this object is impossible, not just improbable; as in its existence would destroy the universe as we know it in an incredibly uncool explosion of logic.

So what does this have to do with Atheism? Well, let's say we come across a particularly amazing philosopher. If he can clearly define what we mean by "God" (thank you Cletus) and definitively show that it is internally inconsistent (anyone care to try?), than he has disproven the existence of said "God."